Studies in Applied Mathematics最新文献

{"title":"Spatial Movement With Explicit Memory and Nonlocal Pregnancy Delay","authors":"Xiaoxi Ding,&nbsp;Hao Shen,&nbsp;Yongli Song","doi":"10.1111/sapm.70011","DOIUrl":"https://doi.org/10.1111/sapm.70011","url":null,"abstract":"<div>\u0000 \u0000 <p>In depicting animal movement, besides considering spatial memory, the pregnancy period of the animals themselves should also be taken into account. This article proposes a novel single-population model with discrete memory delay and nonlocal spatiotemporal gestation delay. Assuming the positive equilibrium is locally stable without spatiotemporal delay, the study investigates two types of directional movements using memory delay and gestation delay as control parameters. The research shows that for the positive memory-based diffusion coefficient, the system destabilizes through homogeneous/nonhomogeneous Hopf bifurcations, but for the negative memory diffusion coefficient, the system not only undergo Hopf bifurcations but also becomes unstable through Turing bifurcations, and may even exhibit Turing–Hopf bifurcation. Finally, we use a diffusive logistic model with predation behavior as an example to numerically simulate the theoretical results and also discover stability switch phenomena.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symmetry Analysis of the Two-Dimensional Stationary Magnetogasdynamics Equations With Coriolis Force in Lagrangian Coordinates","authors":"E. I. Kaptsov,&nbsp;S. V. Meleshko","doi":"10.1111/sapm.70015","DOIUrl":"https://doi.org/10.1111/sapm.70015","url":null,"abstract":"<div>\u0000 \u0000 <p>The paper focuses on symmetry analysis of the two-dimensional stationary magnetogasdynamics equations with Coriolis force in Lagrangian coordinates. This involves the identification of equivalence transformations and the Lie algebra admitted by the equations, and its extensions for various forms of magnetic fields and Coriolis parameter, as well as the construction of group foliations. A considerable part of the work is devoted to group foliations of the magnetogasdynamics equations, extending to the nonstationary isentropic case. The group foliations' approach is typically applied to equations admitting infinite-dimensional groups of transformations, thereby facilitating the simplification of their subsequent analysis. The results obtained in this study generalize previously known findings for the two-dimensional shallow water equations and stationary gas dynamics equations in Lagrangian coordinates. Utilizing the constructed group foliations, invariant solutions are derived for particular forms of the entropy, illustrating the potential for further investigation in this area.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Chebotarov Continua, Jenkins–Strebel Differentials and Related Problems: A Numerical Approach","authors":"M. Bertola","doi":"10.1111/sapm.70016","DOIUrl":"https://doi.org/10.1111/sapm.70016","url":null,"abstract":"<p>We detail a numerical algorithm and related code to construct rational quadratic differentials on the Riemann sphere that satisfy the Boutroux condition. These differentials, in special cases, provide solutions of (generalized) Chebotarov problem as well as being instances of Jenkins–Strebel differentials. The algorithm allows to construct Boutroux differentials with prescribed polar part, thus being useful in the theory of weighted capacity and random matrices.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70016","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Static States for Rotating Two-Component Bose–Einstein Condensates","authors":"Hichem Hajaiej,&nbsp;Xiao Luo,&nbsp;Tao Yang","doi":"10.1111/sapm.70013","DOIUrl":"https://doi.org/10.1111/sapm.70013","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we study static states for rotating two-component Bose–Einstein condensates (BECs) in two and three dimensions. This leads to analyze normalized solutions for a coupled Schrödinger system with rotation. In dimension two, it corresponds to a mass-critical problem, for which we obtain some existence and nonexistence results. In the three-dimensional case, the problem becomes mass-supercritical, where we prove a multiplicity result along with an accurately asymptotical analysis. Furthermore, a stability result is also established in both cases. We not only extend the main results in Ardila and Hajaiej (<i>Journal of Dynamics and Differential Equations</i> 35 (2023), 1643–1665), Arbunich et al. (<i>Letters in Mathematical Physics</i> 109 (2019), 1415–1432), and Luo and Yang (<i>Journal of Differential Equations</i> 304 (2021), 326–347) from the rotating one-component BEC to rotating two-component BECs, but we also partially extend the results of Guo et al. (Discrete and Continuous Dynamical Systems 37 (2017), 3749–3786; <i>Journal of Differential Equations</i> 264 (2018), 1411–1441) from nonrotating two-component BECs to rotating two-component BECs.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of a Reaction–Diffusion–Advection System From River Ecology With Inflow","authors":"Jinyu Wei,&nbsp;Bin Liu,&nbsp;Guoqiang Ren","doi":"10.1111/sapm.70012","DOIUrl":"https://doi.org/10.1111/sapm.70012","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper is to study the population dynamics of a single species model and a two-species competition model from river ecology with inflow. One interesting feature in these models is that species can flow into the river through the upstream end due to advective movement while both diffusive and advective movements will cause population loss at the downstream end. We first determine necessary and sufficient conditions for persistence of a single species, in terms of the critical habitat size and the critical advection rate. For the competition model, we investigate the joint effects of advection rates, interspecific competition intensities, and boundary conditions on global dynamics of the system. It shows that the strategy of smaller advection is beneficial for species to survive. Our results partially extend the previous works.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143115638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Emergence of Well-Ordering and Clustering for a First-Order Nonlinear Consensus Model","authors":"Junhyeok Byeon,&nbsp;Seung-Yeal Ha,&nbsp;Myeongju Kang,&nbsp;Wook Yoon","doi":"10.1111/sapm.70006","DOIUrl":"https://doi.org/10.1111/sapm.70006","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the predictability of asymptotic clustering patterns in a first-order nonlinear consensus model on receiver network on the real line. Nonlinear couplings between particles (agents) are characterized by an odd, locally Lipschitz, and increasing function. The proposed consensus model and its clustering dynamics is motivated by the one-dimensional Cucker–Smale flocking model. Despite the complexity registered by heterogeneous couplings, we provide a sufficient framework to predict asymptotic dynamics such as particles' aggregation, segregation, and clustering patterns. We also verify the robustness of clustering patterns to structural changes such as relativistic effects implemented by the suitable composition of functions.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Traveling Viral Waves for a Spatial May–Nowak Model with Hybrid Local and Nonlocal Dispersal","authors":"Jie Wang,&nbsp;Jinfen Guo,&nbsp;Chuanhui Zhu,&nbsp;Shuang-Ming Wang","doi":"10.1111/sapm.70007","DOIUrl":"https://doi.org/10.1111/sapm.70007","url":null,"abstract":"<div>\u0000 \u0000 <p>To investigate the spatial dynamics of viruses propagating between host cells, the current paper is devoted to studying the existence and nonexistence of viral waves for a reaction–diffusion and May–Nowak system with hybrid dispersal. Specifically, we define a critical wave speed <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>c</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 <annotation>$ c^{ast }$</annotation>\u0000 </semantics></math> threshold to determine the existence of traveling waves when the viral infection reproduction number <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>&gt;</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$ mathcal {R}_{0}&gt;1$</annotation>\u0000 </semantics></math>. By employing the upper/lower solutions along with the Schauder's fixed-point theorem, the existence of traveling waves connecting the uninfected and infected states is determined for each wave speed <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>c</mi>\u0000 <mo>≥</mo>\u0000 <msup>\u0000 <mi>c</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$ cge c^{ast }$</annotation>\u0000 </semantics></math>. Conversely, nonexistence is demonstrated through the application of the negative one-sided Laplace transform for the case <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 <mo>&lt;</mo>\u0000 <mi>c</mi>\u0000 <mo>&lt;</mo>\u0000 <msup>\u0000 <mi>c</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$ 0 &lt; c &lt; c^{ast }$</annotation>\u0000 </semantics></math>. The nonexistence of traveling waves in the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>≤</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$mathcal {R}_{0}le 1$</annotation>\u0000 </semantics></math> case is also demonstrated. Finally, some novel coupled numerical algorithms are developed to analyze the traveling viral waves and asymptotic spreading speed of the model on account of the actual hybrid dispersal features, which strongly shows that the introduction of nonlocal dispersal will accelerate viral infection.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143112379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solving a Singular Limit Problem Arising With Euler–Korteweg Dispersive Waves","authors":"Quentin Didierlaurent,&nbsp;Nicolas Favrie,&nbsp;Bruno Lombard","doi":"10.1111/sapm.70005","DOIUrl":"https://doi.org/10.1111/sapm.70005","url":null,"abstract":"<div>\u0000 \u0000 <p>Phase transition in compressible flows involves capillarity effects, described by the Euler–Korteweg (EK) equations with nonconvex equation of state. Far from phase transition, that is, in the two convex parts of the equation of state, the dispersion terms vanish and one should recover the hyperbolic Euler equations of fluid dynamics. However, the solution of EK equations does not converge toward the solution of Euler equations when dispersion tends toward zero while being nonnull: it is a singular limit problem. To avoid this issue in the case of convex equation of state, a Navier–Stokes–Korteweg (NSK) model is considered, whose viscosity is chosen to counterbalance exactly the dispersive terms. In the limit of small viscosity and small dispersion, the Euler model is recovered. Numerically, an extended Lagrangian method is used to integrate the NSK equations so obtained. Doing so allows to use classical numerical schemes of Godunov type with source term. Numerical results for a Riemann problem illustrate the convergence properties with vanishing dispersion.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143121149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Uniform Asymptotic Expansions for the Zeros of Parabolic Cylinder Functions","authors":"T. M. Dunster,&nbsp;Amparo Gil,&nbsp;Diego Ruiz-Antolin,&nbsp;Javier Segura","doi":"10.1111/sapm.70004","DOIUrl":"https://doi.org/10.1111/sapm.70004","url":null,"abstract":"<div>\u0000 \u0000 <p>The real and complex zeros of the parabolic cylinder function <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>U</mi>\u0000 <mo>(</mo>\u0000 <mi>a</mi>\u0000 <mo>,</mo>\u0000 <mi>z</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$U(a,z)$</annotation>\u0000 </semantics></math> are studied. Asymptotic expansions for the zeros are derived, involving the zeros of Airy functions, and these are valid for <span></span><math>\u0000 <semantics>\u0000 <mi>a</mi>\u0000 <annotation>$a$</annotation>\u0000 </semantics></math> positive or negative and large in absolute value, uniformly for unbounded <span></span><math>\u0000 <semantics>\u0000 <mi>z</mi>\u0000 <annotation>$z$</annotation>\u0000 </semantics></math> (real or complex). The accuracy of the approximations of the complex zeros is then demonstrated with some comparative tests using a highly precise numerical algorithm for finding the complex zeros of the function.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143121150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Auto-Bäcklund Transformations for New Matrix First and Second Painlevé Hierarchies","authors":"Pilar Ruiz Gordoa,&nbsp;Andrew Pickering","doi":"10.1111/sapm.70002","DOIUrl":"https://doi.org/10.1111/sapm.70002","url":null,"abstract":"<div>\u0000 \u0000 <p>We define a new doubly extended matrix second Painlevé hierarchy, and in addition a new extended matrix first Painlevé hierarchy. For the former, we present three auto-Bäcklund transformations (auto-BTs) that constitute nontrivial extensions to our new hierarchy of previously derived results on the auto-BTs of a much simpler matrix second Painlevé hierarchy; for the latter, we define an auto-BT analagous to the third of these matrix second Painlevé auto-BTs. In addition, for both of our new hierarchies, we define a new class of auto-BT. In the scalar reduction, these then give rise to a new Bäcklund process for the second Painlevé equation, as well as to a similar Bäcklund process for the first Painlevé equation. These new Bäcklund processes provide mappings of arbitrary constants appearing in solutions.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143121151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}